Self-Linking, Inflections, and the Normal Euler Class for Smooth and Polyhedral Surfaces in Four-Space

The normal Euler class for a simplicial surface in four-space can be defined by analogy with the geometric description of this class for a smooth surface. We present a combinatorial formula for the normal Euler class in terms of the self-linking numbers of spherical polygons and inflection faces of polyhedra, related to a construction of Gromov, Lawson, and Thurston. The talk will feature computer graphics illustrations.